282 CALCULATING PRODIGIES [CH. XIII 



else, he dreams of them, and sometimes even solves problems 

 in his sleep. His memory is excellent for numbers, but normal 

 or subnormal for other things. At the end of a seance he can 

 repeat the questions which have been put to him and his 

 answers, involving hundreds of digits in all. Nor is his memory 

 in such matters limited to a few hours. Once eight days after 

 he had been given a question on a number of twenty-two 

 digits, he was unexpectedly asked about it, and at once 

 repeated the number. He has been repeatedly examined, and 

 we know more of his work than of any of his predecessors, with 

 the possible exception of Bidder. 



Most of these calculating prodigies find it difficult or im- 

 possible to explain their methods. But we have a few analyses 

 by competent observers of the processes used : notably one by 

 Bidder on his own work ; another by Colburn on his work ; and 

 others by Mtiller and Darboux on the work of Ruckle and 

 Inaudi respectively. That by Bidder is the most complete, and 

 the others are on much the same general lines. 



Bidder's account of the processes he had discovered and 

 used is contained in a lecture* given by him in 1856 to the 

 Institution of Civil Engineers. Before describing these pro- 

 cesses there are two remarks of a general character which 

 should, I think, be borne in mind when reading his statement. 

 In the first place he gives his methods in their perfected form, 

 and not necessarily in that which he used in boyhood : more- 

 over it is probable that in practice he employed devices to 

 shorten the work which he did not set out in his lecture. In 

 the second place it is certain, in spite of his belief to the 

 contrary, that he, like most of these prodigies, had an excep- 

 tionally good memory, which was strengthened by incessant 

 practice. One example will suffice. In 1816, at a performance, 

 a number was read to him backwards : he at once gave it in its 

 normal form. An hour later he was asked if he remembered 



* Institution of Civil Engineers, Proceedings, London, 1856, vol. xv, 

 pp. 251 — 280. An early draft of the lecture is extant in MS. ; the variations 

 made in it are interesting, as showing the history of his mental development, 

 but are not sufficiently important to need detailed notice here. 



